Last year, Skinner - also known as The Streets - said that Allen secretly wants the media attention that she complains about.
Allen took the opportunity to respond while promoting her new album in the US, The Sun reports.
She said: "There's a guy called Mike Skinner who records as The Streets and he did a record that basically talked about how awful it was to be rich and famous. I found that really boring.
"I'm always aware when I'm writing songs that other people have to be able to relate to them."
She added that one track on her new album, 'Not Fair', is about girls being unsatisfied by their boyfriends in bed, which she believes girls can relate to.
Earlier this week, Allen scored a UK double number one, with 'The Fear' being top of the singles chart and It's Not Me, It's You heading the album list.